Functional Solutions for a Plane Problem in Magnetohydrodynamics
Fundamental solutions and asymptotic behaviour for the p-Laplacian equation.
We establish the uniqueness of fundamental solutions to the p-Laplacian equationut = div (|Du|p-2 Du), p > 2,defined for x ∈ RN, 0 < t < T. We derive from this result the asymptotic behavoir of nonnegative solutions with finite mass, i.e., such that u(*,t) ∈ L1(RN). Our methods also apply to the porous medium equationut = ∆(um), m > 1,giving new and simpler proofs of known results. We finally introduce yet another method of proving asymptotic results based on the...
Further studies of fully developed flow through ducts of arbitrary section by the contour line-conformal mapping technique.
Gas exhalation and its calculations. I
Gasdynamic regularity: some classifying geometrical remarks.
Gas-solid reaction with porosity change.
Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation
Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.
Generalized Beltrami flows and other closed-form solutions of an unsteady viscoelastic fluid.
Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation
This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of tridimensional acoustic scattering problems by a smooth closed surface. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be interpreted as generalizations of the well-known Brakhage-Werner [A. Brakhage and P. Werner, Arch....
Generalized Fluid Flows, Their Approximation and Applications.
Generalized function treatment of the Alfvén-gravity wave problem.
Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids
We study a family of non linear schemes for the numerical solution of linear advection on arbitrary grids in several space dimension. A proof of weak convergence of the family of schemes is given, based on a new Longitudinal Variation Diminishing (LVD) estimate. This estimate is a multidimensional equivalent to the well-known TVD estimate in one dimension. The proof uses a corollary of the Perron-Frobenius theorem applied to a generalized Harten formalism.
Generalized Harten Formalism and Longitudinal Variation Diminishing schemes for Linear Advection on Arbitrary Grids
We study a family of non linear schemes for the numerical solution of linear advection on arbitrary grids in several space dimension. A proof of weak convergence of the family of schemes is given, based on a new Longitudinal Variation Diminishing (LVD) estimate. This estimate is a multidimensional equivalent to the well-known TVD estimate in one dimension. The proof uses a corollary of the Perron-Frobenius theorem applied to a generalized Harten formalism.
Generalized lubrification models blow-up and global existence result.
We study a general mathematical model linked with various physical models. Especially, we focus on those models established by King or Spencer-Davis-Voorhees related to thin films extending the lubrication model studied by Bernis-Friedman. According to the initial data, we prove that, either, blow up or global existence can be obtained.
Generalized variational principle for long water-wave equation by He's semi-inverse method.
Generations of waves at an inertial surface due to explosions.
Generic solvability for the 3-D Navier-Stokes equations with nonregular force.
Geometrical methods in hydrodynamics
We describe some recent results on a specific nonlinear hydrodynamical problem where the geometric approach gives insight into a variety of aspects.
Geometrodynamics of some non-relativistic incompressible fluids.
In some previous papers [1, 2] we proposed a geometric formulation of continuum mechanics, where a continuous body is seen as a suitable differentiable fiber bundle C on the Galilean space-time M, beside a differential equation of order k, Ek(C), on C and the assignement of a frame Psi on M. This approach allowed us to treat continuum mechanics as a unitary field theory and to consider constitutive and dynamical properties in a more natural way. Further, the particular intrinsic geometrical framework...
Geometry of fluid motion
We survey two problems illustrating geometric-topological and Hamiltonian methods in fluid mechanics: energy relaxation of a magnetic field and conservation laws for ideal fluid motion. More details and results, as well as a guide to the literature on these topics can be found in [3].